SOLUTION: Hey, I need help with this ASAP if someone could help me with this that would be very much appreciated. Thank you:) a)find all values of b so that x^2 +bx +10 can be factored

Algebra.Com
Question 1173745: Hey, I need help with this ASAP if someone could help me with this that would be very much appreciated. Thank you:)

a)find all values of b so that x^2 +bx +10 can be factored over the integers
b) find all values of b so that 4y^2 +by +5 can be factored over the integers
c) write an algebraic expression for the shaded area. Then write the expression in factored form.
P.S the shaded area is a square the perimeter is x+2 by x+1 and then there is a smaller square inside of that which is 4 by 3.
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.

1)


Start noticing that 10 = 1*10 = 2*5 = (-1)*(-10) = (-2)*(-5).


It gives you all possible values  b = 1   + 10     =   11;

                                      2   +  5     =    7;

                                     (-1) +  (-10) =  -11;

                                     (-2) +  (-5)  =   -7.


Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
(x+5)(x+2), b=7 look at factors of 10.
(x-5)(x-2), b=-7
(x+1)(x+10) b=11
(x-1)(x-10) b=-11
make the discriminant b^2-4ac a perfect square: b^2-40 is a perfect square
-
b^2-80 is a perfect square: b=9,12,21
(2y+1)(2y+5) b=12
(2y-1)(2y-5) b=-12
(4y+1)(y+5) b=21 and the negative
(4y+5)(y+1) b=9 and the negative
-
I'm not clear on the last part.
A perimeter is 2L + 2W, if these are length and width. But in a square they are equal.
Same with a square inside that can't be 4 by 3, at least the way I interpret the statement.
If these are rectangles inside a square with those areas, that needs to be clarified. Something x+2 by x+1 has area x^2+3x+2 and if the 4 by 3 inside is subtracted from the area, the remaining area is x^2+3x-10 which factors into (x+5)(x-2).
RELATED QUESTIONS

hello i would be glad if you could help me with this inequality 2x+1>9 thank you very... (answered by MathTherapy)
I'm stuck on this problem, if someone could please help me, that would be much... (answered by Alan3354)
Will someone PLEASE help me with this. I asked earlier. Thank you I need a 50 word... (answered by solver91311)
I am having a hard time with this problem: 4 1/8 - 1 3/4 If you could help, that would... (answered by ivy12003)
It would be very much appreciated if someone could help me with this, I'm so... (answered by Alan3354)
Okay this is Very confusing to me since I just opened my Algebra book for my online class (answered by richard1234)
Hello, this isn't about Math but I still need help with these 2 questions, and I was... (answered by ankor@dixie-net.com)
Hello, Could you please help me with this problem? Please show me step by step... (answered by lmeeks54)
Hey, I need help with this problem please. I'm really stuck on this. What exactly would... (answered by FrankM)